PLO10 Qc 4h As Ad

You don´t have nutflushdraw blocker, he would not fold flushes if you shove river, he may fold straights and would likely fold two pair, but once he called turn I think he often also has there flushes.
So I would prefer checking back river.

To me more difficult spot would be bet/folding turn. Board is quite drawy and he would likely c/rai sometimes his pair+draw hands and ofcourse straights, so I´m not sure that you can bet any more for value- even to his junky hand you only had 60-40, so I would likely check back turn to then decide river if I want to call his river bet or not

Preflop, you have junk aces in position. 3 betting is fine so long as you have a wider 3 betting range than just aces and kings.

You don't want your opponent to think you have aces when you actually do have aces (and no other way of winning due to an offsuit Q and 4 )

Flop is extremely wet and likely to hit villains range a lot more than he thinks it hits yours. Indeed all you have on the flop is 1 out to the nuts.

If villain has any kind of draw here he wont be folding, and that's a problem for you if you bet the flop because you will have no idea where you are on the turn.

I don't mind checking this flop back but if you do bet the flop and get called, you can't bet the turn. You basically should be giving up at this point rather than bloating the pot even more.